Metamath Proof Explorer

Syntax definition wceq

Description: Extend wff definition to include class equality.

For a general discussion of the theory of classes, see mmset.html#class .

(The purpose of introducing wff A = B here, and not in set theory where it belongs, is to allow us to express, i.e., "prove", the weq of predicate calculus in terms of the wceq of set theory, so that we do not "overload" the = connective with two syntax definitions. This is done to prevent ambiguity that would complicate some Metamath parsers. For example, some parsers - although not the Metamath program - stumble on the fact that the = in x = y could be the = of either weq or wceq , although mathematically it makes no difference. The class variables A and B are introduced temporarily for the purpose of this definition but otherwise not used in predicate calculus. See df-cleq for more information on the set theory usage of wceq .)

Ref Expression
Assertion wceq
wff A = B